The reasoning and conclusions of the evolutionary theory of games are based on the hypothesis that each strategist reproduces its own kind. Using digenic variants of the Hawk-Dove-Bourgeois game, we illustrate the fact that the transposition of this type of approach to sexual diploid populations, for which the evolutionary theory of games also initially attempted to explain, is not quite straightforward. It is clear that a pure ESS cannot be reached if it is solely dependent on heterozygotes. However, more unexpectedly, the fact that an ESS can be reached does not guarantee the absence of alternative attractors, not fulfilling ESS conditions, thereby involving a genetic load for the populations.